IRR Calculator

What the rate represents

The internal rate of return is the discount rate at which a cash flow stream's net present value comes to zero: the single annual rate that makes what comes back exactly balance what went out, once the timing of each amount is accounted for. It is a property of the flows themselves rather than a comparison against anything, which is why it can be quoted without naming a hurdle. Comparing it against one is a separate step: a rate above the required return corresponds to a positive net present value at that return, and a rate below it to a negative one. That correspondence holds for a stream shaped like this one (a single outflow followed by inflows) and stops being reliable where the flows change sign more than once, since several rates can then satisfy the same equation.

The identity behind the default figures

Where the terminal value equals the initial outlay, the rate is simply the annual cash flow as a share of that outlay, whatever the term. The capital comes back whole at the end, so the annual flow is pure yield on an unchanged principal, the same arithmetic as a bond held to redemption at par. That is why the defaults on this page return exactly the cash flow divided by the outlay, and why changing the number of years moves the result by nothing at all: verified at one, three, ten, twenty-five and forty years, all identical. It also explains why the What-If block shows no card for the term.

Away from that configuration the term matters a great deal, because the capital has to be recovered out of the flows themselves. With the same outlay and cash flow but no terminal value, the rate runs from below zero at five years to 8.14% at ten and 13.89% at twenty: the same annual receipt, three very different answers, decided entirely by how long it keeps arriving.

What moves the number most

Measured at the default ratios (an annual flow of 15% of the outlay and a terminal value equal to it), the ordering is clear and holds at any scale or currency, since the rate depends only on those ratios and the term. The initial outlay is the largest lever and an asymmetric one: 10% less lifts the rate by 2.16 points while 10% more cuts it by 1.85. The cash flow is exactly linear at these settings, moving the rate by 1.5 points in either direction for a 10% change, which follows directly from the identity above. The terminal value is the smallest, at 0.50 down and 0.48 up. The term behaves differently from the other three. It does not move the result at all while the terminal value equals the outlay, and its pull grows the further the terminal value sits from that point, as a gradient rather than a switch. It also changes direction there: below that point, more years raise the rate, because the flows are what has to recover the capital the exit does not return; above it, more years lower the rate, because the gain waiting at the end is spread across a longer holding. Holding the outlay and the cash flow at their defaults, an extra year is worth +1.29 points with no terminal value, +0.49 at half the outlay, nothing at all when the two match, and −0.36 at one-and-a-half times it. On the same 10% test, the term only overtakes the terminal value as the larger of the two levers once the terminal value has fallen to somewhere between 61% and 66% of the outlay, a band rather than a point, because nudging the two inputs up gives a different answer from nudging them down. That band belongs to this particular shape, not to the measure: it is where the crossing sits for a 15% annual flow over ten years, and it moves with the size of the flow, sitting nearer 48–52% of the outlay when the flow is 5% and nearer 74–81% when it is 40%. It is unchanged by scale and by currency, since only the ratios matter.

When more than one rate solves the equation

A cash flow stream can have as many candidate rates as it has changes of sign, which is the standard caution attached to this measure. It does not arise in what this calculator models: a single outflow followed by inflows changes sign once, so the equation has one solution and the solver converges on it. Streams that alternate (a project needing further capital part-way through, or one with a clean-up cost at the end) can produce several, and there the rate stops being a single number and needs either a modified variant or a direct comparison of present values instead.

The reinvestment question

The measure is commonly described as assuming intermediate cash flows are reinvested at the rate itself, which would be an optimistic assumption for a high figure. That description is disputed: the rate is a discount rate that solves an equation, and nothing in the arithmetic instructs anything to be reinvested anywhere. What is agreed is that comparing two projects on this measure alone says nothing about what happens to money as it comes back, and that a modified variant exists precisely because the reinvestment assumption is the point at issue for some users.

What this and net present value each measure

One returns a rate, the other an amount, and the difference matters because amounts add across a portfolio and rates do not. A large project at a modest rate can create more total value than a small one at a high rate, so the two measures rank differently whenever size differs, and the rate carries no information about how much capital is earning it. They also part company on the reinvestment question above, and where cash flows change sign more than once. A rate is also easier to quote and compare in conversation than an amount tied to one particular size of project.

Reading a rate in context

A rate on its own carries no scale: what counts as high depends on the risk taken, the illiquidity accepted, and the period over which it was earned. The conventional comparisons are against a low-risk alternative, against a benchmark for the same asset class over the same period, and against the return required to justify the risk. Published expectations for any asset class differ by source, by market and by era, so a threshold taken from one context does not carry to another. This calculator produces the rate; the comparison is not something it can supply.

What this calculator models

One outflow at the start, an equal cash flow at the end of each year, and a terminal value added to the final year. That shape covers a holding bought once, yielding steadily and sold at the end, and nothing else. Uneven or lumpy flows, a gap year, mid-year timing, a second outflow part-way through, fees, taxes and inflation are all outside it. Flows that give back less than the outlay are still solvable and return a rate below zero; only where nothing comes back at all does the calculator report that no rate solves the equation, rather than returning the edge of its search range.